Abstract:
When modelling biological systems, one of first changes for a mathematician,
computer scientist, or modeler of any stripes is coming to terms with the
empirical reality of those systems. As an illustrative example, one of the
most wonderful and (historically) mysterious aspects of disease is our bodies
ability to remember old infections, so we never get sick from diseases like
measles more than once. Yet for some diseases, like pertussis, tuberculosis,
and HIV, memory seems more complex, and to this day, many research dollars go
into understanding exactly how the creation and maintenance of immune memory
works. Some good model-based theories may help us make sense of the situation,
but to get there, we first have to travel a winding road through genetics, cell
biology, physiology, and epidemiology.

Abstract:
The interactions of ions flowing through biological systems has been a central
topic in biology for more than 100 years. Flows of ions produce signaling in
the nervous system, initiation of contraction in muscle, coordinating the
pumping of the heart and regulating the flow of water through kidney and
intestine.

Ion concentrations inside cells are controlled by ion channels through the
lipid membrane. In this talk, I will propose a continuum model that is derived
from the energetic variational approach which include the coupling between the
electrostatic forces, the hydrodynamics, diffusion and crowding (due to the
finite size effects). The model provides some basic understanding of one of
the most important properties of proteins, the ion selectivity.

This is a joint work with Yunkyong Hyon (IMA), Taichia Lin (National Taiwan
University) and Robert Eisenberg (Rush Medical School).

Title:
The effects of multi-scale dynamics on the ecology and evolution of an insect virus.

Abstract:
A challenge to understanding infectious disease ecology is that processes
occurring at multiple scales likely impact the ecological and evolutionary
patterns found in nature. Both pathogen growth within hosts and pathogen
transmission between hosts are likely important to pathogen dynamics, but
studies typically focus on only one of these scales or the other. An integrated
approach to disease modeling may thus provide novel insights. The challenge to
using an integrated approach is that within-host dynamics are particularly
poorly studied, because of difficulties associated with directly tracking
pathogen dynamics within hosts. Here we demonstrate a method by which pathogen
growth within hosts can be inferred through fitting mechanistic birth-death
models to easily collectable dose-response data, alleviating the need to
directly track pathogen dynamics over time. We then use this method to test
various models of baculovirus growth in gypsy moth (Lymantria dispar) hosts, to
identify the biological mechanisms important to pathogen growth in this system.
This analysis yields novel insights into the ecology and evolution of the gypsy
moth and its baculovirus with implications for strategies to control gypsy moth
population outbreaks. Furthermore, this analysis reveals that host differences
alone are insufficient to explain the observed variability in host outcomes,
and that demographic stochasticity in pathogen growth is likely important in
explaining this variability. The importance of demographic stochasticity, in
turn, suggests that genetic drift may occur during pathogen growth within
hosts. We next combine our birth-death model of baculovirus growth within hosts
with a stochastic SEIR disease model that describes transmission dynamics
between hosts for this insect baculovirus, and we use this nested model to
explore the importance of genetic drift on pathogen diversity within hosts.
Using reasonable parameter values, our model predicts that genetic diversity
within hosts will be strongly affected by the drift that occurs both during
pathogen population bottlenecks at transmission, and during the subsequent
population growth of pathogen within hosts. We next compare the levels of
pathogen diversity within hosts predicted by the models to Illumina sequence
data from 223 field-collected hosts. This analysis shows that genetic drift is
indeed important to explaining the observed patterns of pathogen diversity. We
take this as evidence that genetic drift occurring within hosts is important to
understanding patterns in disease ecology, suggesting that stochasticities that
act both within hosts and be- tween hosts need to be accounted for to
understand pathogen evolution in general. We then discuss the implications of
these findings for evolution of virulence theory and host-pathogen
interactions.

Date:
Thursday, September 20, 2012

No talk this week.

Date:
Thursday, September 27, 2012

Speaker: Hong Qian, from the University of Washington Department of Applied Mathematics.

Abstract:
Agent-based population dynamics articulates a distribution in the behavior of
individuals and considers deterministic behavior at the population level as an
emergent phenomenon. Using chemical species inside a small aqueous volume as an
example, we introduce Delbruck-Gillespie birth-and-death process for chemical
reactions dynamics. Using this formalism, we (1) illustrate the relation
between nonlinear saddle-node bifurcation and first-order phase transition;
(2) introduce a thermodynamic theory for entropy and entropy production and
prove 1st and 2nd Laws of Thermodynamics as theorems; (3) show how an
analytical mechanics (i.e., Lagrangian and Hamiltonian systems) arises and the
meaning of kinetic energy. We suggest the inter-attractoral stochastic
dynamics as a possible mechanism for isogenetic variations in cellular biology.

Abstract:
Biological protein pores and pore-forming peptides can generate a pathway for the flux of ions and other charged and polar species across otherwise impermeable cellular membranes. In nature, these nanopores have diverse and essential functions that range from maintaining cell homeostasis and participating in cell signaling to activating or killing cells. The combination of nano-scale dimensions and inherent sophisticated functionality of these biological pores have them made particularly attractive for the growing field of bionanotechnology where their applications range from single-molecule sensing to drug delivery and targeted killing of malignant cells. Recently, nano-scale pores fabricated in synthetic materials have also emerged as powerful platforms for single-molecule sensing and characterization. In this talk, I present two examples of application of biological and synthetic nanopores for detection and characterization of molecular processes on lipid membranes. In the first example, we applied an ion channel-forming peptide, gramicidin A, for sensing and detection of membrane-associated enzymatic activities and binding interactions. In the second example, we modified a synthetic nanopore by coating its walls with non-fouling lipid bilayers to enable sensing and characterization of single protein molecules as well as molecular processes on lipid bilayers.

Date:
Thursday, October 18, 2012

Speaker:
Huijing Du from Notre Dame University.

Title:
Multiscale modeling of Pseudomonas aeruginosa swarming

Abstract:
Many bacteria move in groups, in a mode described as swarming, to
colonize surfaces and form biofilms to survive external stresses. One
such bacterium is Pseudomonas aeruginosa, which often, but not always,
forms branched tendril patterns during swarming; this phenomena occurs
only when bacteria produce rhamnolipid, which is regulated by
population-dependent signaling called quorum sensing. The experimental
results of this work show that P. aeruginosa cells propagate as high
density waves that move symmetrically as rings within swarms toward
the extending tendrils. Biologically justified cell-based multiscale
model simulations suggest a mechanism of wave propagation as well as a
branched tendril formation at the edge of the population that depends
upon competition between the changing viscosity of the bacterial
liquid suspension and the liquid film boundary expansion caused by
Marangoni forces. Therefore, P. aeruginosa efficiently colonizes
surfaces by controlling the physical forces responsible for expansion
of thin liquid film and by propagating toward the tendril tips. The
model predictions of wave speed and swarm expansion rate as well as
cell alignment in tendrils were confirmed experimentally. The study
results suggest that P. aeruginosa responds to environmental cues on a
very short timescale by actively exploiting local physical phenomena
to develop communities and efficiently colonize new surfaces.

Title:
How does pathological behavior arise in the Kv6.4 knockout mouse?

Abstract:
We are characterizing central and peripheral behaviors in a
potassium channel knockout mouse (Kv6.4 KO). The mouse has behavioral
deficits consistent with disrupted signaling in brain regions in which the
Kv6.4 gene is expressed. Kv6.4 is a regulatory subunit that enhances channel
activation but paradoxically decreases K+ current size in vitro. It is
therefore difficult to predict the neuronal K+ current phenotype of Kv6.4 KO
in vivo. We are using a combination of biophysical, behavioral and patch
clamp analysis to quantitatively describe the neurophysiological changes
that occur following Kv6.4 KO.

Abstract:
The integrate and fire model for time evolution of potentials in neuronal
cells goes back to Lapicque in 1907. In 2002 a discrete model was defined by
Eurich, Hermann and Ernst, which is the starting point of the discussion in
this talk. I will shortly describe the neurophysiological basis and then
present a random dynamical model for its description. In particular, I will
concentrate on the avalanche size distribution and the associated power law.
This law is conjectured to be of order 3/2 and I will give mathematical
rigorous arguments for it, one based on branching processes, another based on
Cayley's theorem for the number of trees with a given number of vertices.

Date:
Thursday, November 15, 2012

Speaker:
Colin Campbell, Postdoc in Biology

Title:
A dynamic model of cancerous tumor pathogenesis

Abstract:
CD8+ T cells play an important role in determining cancer pathogenesis. In this
talk I will discuss a dynamic model of the interactions between CD8+ T cells
and cancerous tumors of the brain, pancreas, and bones. The model replicates
five categories of response ranging ranging from tumor clearance to
unrestrained tumor growth, and several predictions from the model have been
experimentally confirmed. Importantly, the model highlights differences in
apoptosis rates that contribute to compromised CD8+ T cell responses and tumor
progression, knowledge of which is essential for development of cancer
immunotherapy. I will focus the talk on the mathematical model, specifically
(1) the biological and mathematical motivations for its form and (2) the
relationship between the parameter space and resulting dynamic behavior.

Abstract:
As the title implies, my work focuses on applying stochastic processes to
biological problems. All living organisms are made up of cells, and cells -
from single-celled bacteria to neurons within the human brain - have a single
common feature: they are small. A typical cell is about 10 micrometers in
diameter, which is 20 times less than the width of a human hair. Despite its
size, a cell must organize and process massive amounts of information stored
within in DNA and use this information to perform the many functions necessary
to obtain energy, reproduce, and adapt to its environment - all while competing
with other species. Indeed, their microscopic size creates an interesting
challenge because thermal fluctuations become significant. When thermal
fluctuations constantly bombard the delicate cellular machinery, its behavior
becomes unpredictable and random. Cells have not simply learned to overcome
this difficulty, to function in spite of random fluctuations, they have learned
to exploit and use it to their advantage. In my talk, I will discuss a few of
these mechanisms and how their use by neurons is important for learning and
memory.

Date:
Thursday, December 6, 2012

Speaker:
Nicole Mideo

Title:
Bridging scales in the evolution of infectious disease life histories

Abstract:
Although parasite fitness is often equated with between-host transmission, such
a simple assumption overlooks the fact that transmission is a consequence of
processes acting on at least two different biological scales: within and
between hosts. Studying the evolution of disease life histories (e.g., patterns
of virulence and transmission over the course of an infection) therefore
requires an understanding of the interactions between parasites, host
resources, and immunity at the within-host level; of parasite transmission,
host demography, and epidemiology at the between-host level; and of the links
between levels. Mathematically, there is a straightforward way to nest models
of within-host dynamics into between-host models for studying disease life
history evolution. However, for many parasites the required mechanistic details
of the within-host dynamics are often unknown, so generating evolutionary
predictions is not possible. I will present an alternative,
function-valued trait' approach that allows for interactions between
scales without requiring a mechanistic within-host model. Instead, this
approach captures constraints at the within-host level phenomenologically,
through estimates of genetic covariance functions. I will demonstrate how this
approach works, in principle, by applying it to data from experimental rodent
malaria infections, and reveal how patterns of covariance can interact with
epidemiological dynamics to affect the evolutionary trajectories of disease
life history traits.